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Stella · 2024年06月23日

关于goal2的一个简便算法

  1. CFA III
  2. Asset Allocation

* 问题详情，请 查看题干

NO.PZ201803130100000602

问题如下：

Construct the overall goals-based asset allocation for the Armstrongs given their three goals and Abbott’s suggestion for investing any excess capital. Show your calculations.

Show your calculations.

选项：

解释：

Guideline Answer:
■ The module that should be selected for each goal is the one that offers the highest return given the time horizon and required probability of success.
■ Approximately 16.4%, 12.7%, 50.4%, and 20.5% should be invested in Modules A, B, C, and D, respectively. The appropriate goals-based allocation for the Armstrongs is as follows:


Supporting calculations:
For Goal 1, which has a time horizon of five years and a required probability of success of 85%, Module C should be chosen because its 4.4% expected return is higher than the expected returns of all the other modules. The present value of Goal 1 is calculated as follows:
N = 5, FV = –5,000,000, I/Y = 4.4%; CPT PV = $4,031,508 (or $4.03 million)
So, approximately 50.4% of the total assets of $8 million (= $4.03 million/$8.00 million) should be allocated to Module C.

For Goal 2, which has a time horizon of 10 years and a required probability of success of 99%, Module B should be chosen because its 2.2% expected return is higher than the expected returns of all the other modules. The present value of Goal 2 is calculated as follows:

PV=$100,000/(1.022)1+$100,000(1.03)1/(1.022)2+$100,000(1.03)2/(1.022)3+...+$100,000(1.03)9/(1.022)10

PV = $1,013,670 (or $1.01 million)

So, approximately 12.7% of the total assets of $8 million (= $1.01 million/$8.00 million) should be allocated to Module B.

For Goal 3, which has a time horizon of 25 years and a required probability of success of 75%, Module D should be chosen because its 7.5% expected return is higher than the expected returns of all the other modules. The present value of
Goal 3 is calculated as follows:
N = 25, FV = –10,000,000, I/Y = 7.5%; CPT PV = $1,639,791 (or $1.64 million)
So, approximately 20.5% of the total assets of $8 million (= $1.64 million/$8.00 million) should be allocated to Module D.

Finally, the surplus of $1,315,032 (= $8,000,000 – $4,031,508 – $1,013,670 –$1,639,791), representing 16.4% (= $1.32 million/$8.00 million), should be invested in Module A following Abbott’s suggestion.

想到一个简便算法，辛苦老师帮忙看看是否可以适用其他情况

1.首先知道生活费需要是先付年金形式，调整计算器之后pmt=-100000，I/Y=-0.78,N=10,FV=0,算出pv=1036127.84

由于是从第二年末inflation才开始调整的，所以I/Y=-0.78对应的调整之后的数据，而本身还有一年2.2%未计算进去，所以还需要再多除一个（1+2.2%）

通过数据验证是没问题的，所以想看看这种取巧的方法能否在之后其他类似的题中推广，也就不存在理解起来比较费劲的问题了

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已采纳答案

Lucky_品职助教 · 2024年06月24日

嗨，努力学习的PZer你好：


同学你好：


你的算法没有问题，何老师对这道题的 goal2 算法的讲解，和你的计算方式是一致的（见下面截图），这道题给出的答案可以不用参考，因为完全不具备可参考性。




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努力的时光都是限量版，加油！

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NO.PZ201803130100000602 问题如下 Construtheoverall goals-baseasset allocation for the Armstrongs given their three goalsanAbbott’s suggestion for investing any excess capital. Show yourcalculations.Show your calculations. Guiline Answer:■ The mole thshoulselectefor eagois the one thoffers the highest return given the time horizon anrequireprobability of success.■ Approximately 16.4%, 12.7%, 50.4%, an20.5% shoulinvestein Moles an respectively. The appropriate goals-baseallocation for the Armstrongs is follows:Supporting calculations:For Go1, whiha time horizon of five years ana requireprobability of success of 85%, Mole C shoulchosen because its 4.4% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go1 is calculatefollows:N = 5, FV = –5,000,000, I/Y = 4.4%; CPT PV = $4,031,508 (or $4.03 million)So, approximately 50.4% of the totassets of $8 million (= $4.03 million/$8.00 million) shoulallocateto Mole For Go2, whiha time horizon of 10 years ana requireprobability of success of 99%, Mole B shoulchosen because its 2.2% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go2 is calculatefollows:PV=$100,000/(1.022)1+$100,000(1.03)1/(1.022)2+$100,000(1.03)2/(1.022)3+...+$100,000(1.03)9/(1.022)10PV = $1,013,670 (or $1.01 million)So, approximately 12.7% of the totassets of $8 million (= $1.01 million/$8.00 million) shoulallocateto Mole For Go3, whiha time horizon of 25 years ana requireprobability of success of 75%, Mole shoulchosen because its 7.5% expectereturn is higher ththe expectereturns of all the other moles. The present value ofGo3 is calculatefollows:N = 25, FV = –10,000,000, I/Y = 7.5%; CPT PV = $1,639,791 (or $1.64 million)So, approximately 20.5% of the totassets of $8 million (= $1.64 million/$8.00 million) shoulallocateto Mole Finally, the surplus of $1,315,032 (= $8,000,000 – $4,031,508 – $1,013,670 –$1,639,791), representing 16.4% (= $1.32 million/$8.00 million), shoulinvestein Mole A following Abbott’s suggestion. 老师，首先请帮忙看一下我的答案这样写OK吗？Accorng to the answer of last question, we shoulchoose mole C for go1, mole B for go2 anmole for goal3.We shoulcalculate the present value of these liabilities first with the expectereturns of eaportfolio.For go1: PV=5/(1+4.4%)^5=4.03 millionFor go2: PV=0.1/(1+2.2%)+0.1*(1+3%)/(1+2.2%)^2+……=1.01millionFor go3: PV=10/(1+7.5%)^25=1.64millionTotamount equals to 6.68millionThe resicapitis 1.32million anshoulallocateto mole A Abbott suggests. In conclusion the overall capitallocation weights are 16.5%for mole 12.6% for mole 50.4% for mole C an20.5% for sub-portfolio 就是写的比较简练，没有答案中那么长，再一个就是我最后算出来的占比和答案存在0.01%的尾差，考试的时候会扣分吗？谢谢！

2024-10-03 13:56 1 · 回答

NO.PZ201803130100000602 问题如下 Construtheoverall goals-baseasset allocation for the Armstrongs given their three goalsanAbbott’s suggestion for investing any excess capital. Show yourcalculations.Show your calculations. Guiline Answer:■ The mole thshoulselectefor eagois the one thoffers the highest return given the time horizon anrequireprobability of success.■ Approximately 16.4%, 12.7%, 50.4%, an20.5% shoulinvestein Moles an respectively. The appropriate goals-baseallocation for the Armstrongs is follows:Supporting calculations:For Go1, whiha time horizon of five years ana requireprobability of success of 85%, Mole C shoulchosen because its 4.4% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go1 is calculatefollows:N = 5, FV = –5,000,000, I/Y = 4.4%; CPT PV = $4,031,508 (or $4.03 million)So, approximately 50.4% of the totassets of $8 million (= $4.03 million/$8.00 million) shoulallocateto Mole For Go2, whiha time horizon of 10 years ana requireprobability of success of 99%, Mole B shoulchosen because its 2.2% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go2 is calculatefollows:PV=$100,000/(1.022)1+$100,000(1.03)1/(1.022)2+$100,000(1.03)2/(1.022)3+...+$100,000(1.03)9/(1.022)10PV = $1,013,670 (or $1.01 million)So, approximately 12.7% of the totassets of $8 million (= $1.01 million/$8.00 million) shoulallocateto Mole For Go3, whiha time horizon of 25 years ana requireprobability of success of 75%, Mole shoulchosen because its 7.5% expectereturn is higher ththe expectereturns of all the other moles. The present value ofGo3 is calculatefollows:N = 25, FV = –10,000,000, I/Y = 7.5%; CPT PV = $1,639,791 (or $1.64 million)So, approximately 20.5% of the totassets of $8 million (= $1.64 million/$8.00 million) shoulallocateto Mole Finally, the surplus of $1,315,032 (= $8,000,000 – $4,031,508 – $1,013,670 –$1,639,791), representing 16.4% (= $1.32 million/$8.00 million), shoulinvestein Mole A following Abbott’s suggestion. 1.这里的inflation rate 可以算到分母上去吗？还是一定要算到分子上？2.这里的折现率为什么可以直接用表格里的

2024-05-02 14:12 1 · 回答

NO.PZ201803130100000602 问题如下 Construtheoverall goals-baseasset allocation for the Armstrongs given their three goalsanAbbott’s suggestion for investing any excess capital. Show yourcalculations.Show your calculations. Guiline Answer:■ The mole thshoulselectefor eagois the one thoffers the highest return given the time horizon anrequireprobability of success.■ Approximately 16.4%, 12.7%, 50.4%, an20.5% shoulinvestein Moles an respectively. The appropriate goals-baseallocation for the Armstrongs is follows:Supporting calculations:For Go1, whiha time horizon of five years ana requireprobability of success of 85%, Mole C shoulchosen because its 4.4% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go1 is calculatefollows:N = 5, FV = –5,000,000, I/Y = 4.4%; CPT PV = $4,031,508 (or $4.03 million)So, approximately 50.4% of the totassets of $8 million (= $4.03 million/$8.00 million) shoulallocateto Mole For Go2, whiha time horizon of 10 years ana requireprobability of success of 99%, Mole B shoulchosen because its 2.2% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go2 is calculatefollows:PV=$100,000/(1.022)1+$100,000(1.03)1/(1.022)2+$100,000(1.03)2/(1.022)3+...+$100,000(1.03)9/(1.022)10PV = $1,013,670 (or $1.01 million)So, approximately 12.7% of the totassets of $8 million (= $1.01 million/$8.00 million) shoulallocateto Mole For Go3, whiha time horizon of 25 years ana requireprobability of success of 75%, Mole shoulchosen because its 7.5% expectereturn is higher ththe expectereturns of all the other moles. The present value ofGo3 is calculatefollows:N = 25, FV = –10,000,000, I/Y = 7.5%; CPT PV = $1,639,791 (or $1.64 million)So, approximately 20.5% of the totassets of $8 million (= $1.64 million/$8.00 million) shoulallocateto Mole Finally, the surplus of $1,315,032 (= $8,000,000 – $4,031,508 – $1,013,670 –$1,639,791), representing 16.4% (= $1.32 million/$8.00 million), shoulinvestein Mole A following Abbott’s suggestion. PV2 = 1067212 13.34% I/Y = （1+2.2%）/（1+3%）-1 = -0.78%PMT = 100000 * 1.03 = 103000N = 10FV = 0这为什么错了呢

2024-02-09 14:42 1 · 回答

NO.PZ201803130100000602 问题如下 Construtheoverall goals-baseasset allocation for the Armstrongs given their three goalsanAbbott’s suggestion for investing any excess capital. Show yourcalculations.Show your calculations. Guiline Answer:■ The mole thshoulselectefor eagois the one thoffers the highest return given the time horizon anrequireprobability of success.■ Approximately 16.4%, 12.7%, 50.4%, an20.5% shoulinvestein Moles an respectively. The appropriate goals-baseallocation for the Armstrongs is follows:Supporting calculations:For Go1, whiha time horizon of five years ana requireprobability of success of 85%, Mole C shoulchosen because its 4.4% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go1 is calculatefollows:N = 5, FV = –5,000,000, I/Y = 4.4%; CPT PV = $4,031,508 (or $4.03 million)So, approximately 50.4% of the totassets of $8 million (= $4.03 million/$8.00 million) shoulallocateto Mole For Go2, whiha time horizon of 10 years ana requireprobability of success of 99%, Mole B shoulchosen because its 2.2% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go2 is calculatefollows:PV=$100,000/(1.022)1+$100,000(1.03)1/(1.022)2+$100,000(1.03)2/(1.022)3+...+$100,000(1.03)9/(1.022)10PV = $1,013,670 (or $1.01 million)So, approximately 12.7% of the totassets of $8 million (= $1.01 million/$8.00 million) shoulallocateto Mole For Go3, whiha time horizon of 25 years ana requireprobability of success of 75%, Mole shoulchosen because its 7.5% expectereturn is higher ththe expectereturns of all the other moles. The present value ofGo3 is calculatefollows:N = 25, FV = –10,000,000, I/Y = 7.5%; CPT PV = $1,639,791 (or $1.64 million)So, approximately 20.5% of the totassets of $8 million (= $1.64 million/$8.00 million) shoulallocateto Mole Finally, the surplus of $1,315,032 (= $8,000,000 – $4,031,508 – $1,013,670 –$1,639,791), representing 16.4% (= $1.32 million/$8.00 million), shoulinvestein Mole A following Abbott’s suggestion. 老师，go2在求present value是 计算器有没有快捷算法，按照解析给的公式，考试根本不可能算出来。

2024-01-31 21:18 1 · 回答